TY - JOUR
T1 - On the extent of star countable spaces
AU - Alas, O.T.
AU - Junqueira, L.R.
AU - van Mill, J.
AU - Tkachuk, V.V.
AU - Wilson, R.G.
PY - 2011
Y1 - 2011
N2 - For a topological property P, we say that a space X is star P if for every open cover U of the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω
AB - For a topological property P, we say that a space X is star P if for every open cover U of the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω
U2 - 10.2478/s11533-011-0018-y
DO - 10.2478/s11533-011-0018-y
M3 - Article
SN - 1895-1074
SP - 603
EP - 615
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
ER -